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There are 12 men at a dance. How many ways are there to pair off eight women at the dance with eight of these 12 men?

Discrete Math
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This is what I have so far. Thank you in advance. (a) no. of ways=12c8=12c(12-8)=12c4=12*11*10*9/(4*3*2*1)=11*5*9=495 (b) no. of ways 8 men can be selected to form pairs with women=12c8=495 8 women can be selected in ways=8! total no of ways=495*8!
I do not believe part a is right, I have already gotten a different answer for that. But thank you!
normal choice question , you have 12 men to choose from , and 8 places to put them, and the arrangement differs with the same selection of men ( same women with a different man ) so its 12P8

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Other answers:

12c8 would be the number of ways of selecting which men get to dance. It is 12p8.

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